[Paper Review] Pionic couplings to the lowest heavy-light mesons of positive and negative parity

Damir Bečirević, Emmanuel Chang+1 more|arXiv (Cornell University)|Mar 1, 2012

Quantum Chromodynamics and Particle Interactions19 references3 citations

TL;DR

This paper presents the first lattice QCD computation of the pionic coupling $ h $, alongside $ \hat{g} $ and $ \widetilde{g} $, for heavy-light mesons in the static quark limit using $ N_f = 2 $ dynamical Wilson-Clover quarks. By computing the radial distribution of the axial current matrix element between pseudoscalar and scalar mesons, the authors extract $ h $, resolving a long-standing challenge in accessing the soft pion limit for transitions between different doublets. The key result is $ h = 0.71(2)(9) $ (Set 1) and $ h = 0.60(2)(4) $ (Set 2&3), with hierarchy $ \widetilde{g} < \hat{g} < h $.

ABSTRACT

We present the method and compute the strong couplings of the lowest and first orbitally excited heavy-light mesons to a soft pion in the static heavy quark limit on the lattice. Besides the usual g^ and g couplings, we were able to make the first computation of the coupling h using the relevant radial distributions. Our results are obtained from the simulations of QCD with Nf=2 light Wilson-Clover quarks, combined with the improved static quark actions. The hierarchy among couplings that emerges from our study is g &lt; g^ &lt; h.

Motivation & Objective

• To compute the pionic coupling $ h $, which parameterizes the $ B_0^* \to B\pi $ decay amplitude, in the static heavy quark limit.
• To resolve the difficulty in accessing the soft pion limit ($ q^2 \to 0 $) for transitions between different heavy-light meson doublets.
• To compute $ \hat{g} $ and $ \widetilde{g} $ couplings for consistency and to enable combined chiral extrapolation.
• To validate the method by comparing radial distributions with quark model predictions, confirming qualitative and quantitative agreement.
• To provide lattice results for $ h $, $ \hat{g} $, and $ \widetilde{g} $ that can guide chiral extrapolations in $ B $-physics lattice calculations.

Proposed method

• Compute the radial distribution of the light quark axial current matrix element between the pseudoscalar $ B $ and scalar $ B_0^* $ mesons using lattice QCD with $ N_f = 2 $ dynamical Wilson-Clover quarks.
• Use the radial distribution to extract the form factor $ A_+ $ at finite momentum transfer $ \Delta_q^2 $, then extrapolate to $ q^2 = 0 $ to obtain the coupling $ h = A_+(0) $.
• Apply the improved static quark action with HYP (hyper-cubic) blocking on the Wilson line to enhance the accuracy of the heavy quark propagator.
• Perform chiral extrapolation using data from multiple $ \kappa_q $ values and lattice spacings, combining results from different gauge actions (Iwasaki and Wilson plaquette).
• Use moment expansion of the radial distribution to cross-check the $ h $-coupling extraction via $ R_\Delta $ and $ R_4 $, ensuring consistency.
• Symmetrize systematic errors from chiral extrapolation to report final results with combined statistical and systematic uncertainties.

Experimental results

Research questions

• RQ1 Can the pionic coupling $ h $, which governs transitions between different heavy-light meson doublets (e.g., $ B_0^* \to B\pi $), be computed reliably in the static heavy quark limit on the lattice?
• RQ2 What is the hierarchy among the couplings $ \widetilde{g} $, $ \hat{g} $, and $ h $, and does it match theoretical expectations?
• RQ3 How can the soft pion limit ($ q^2 \to 0 $) be accessed for matrix elements involving mesons from different doublets, given the numerical challenges in reaching $ q^2 = 0 $?
• RQ4 To what extent do the radial distributions of the axial current matrix element agree with quark model predictions?
• RQ5 How do the couplings $ h $, $ \hat{g} $, and $ \widetilde{g} $ behave under chiral extrapolation, and what is their impact on $ B $-physics form factor calculations?

Key findings

• The coupling $ h $, which parameterizes the $ B_0^* \to B\pi $ decay amplitude, is computed for the first time in lattice QCD using the radial distribution method, resolving a long-standing challenge.
• The value of $ h $ is found to be $ 0.71(2)(9) $ for the Iwasaki gauge action (Set 1) and $ 0.60(2)(4) $ for the Wilson plaquette action (Sets 2 & 3), with systematic errors symmetrized.
• The hierarchy among couplings is established as $ \widetilde{g} < \hat{g} < h $, with $ \widetilde{g} = -0.19(2)(1) $, $ \hat{g} = 0.47(1)(6) $, and $ h = 0.71(2)(9) $ in Set 1.
• The radial distributions of the axial current matrix element show striking quantitative agreement with predictions from two classes of quark models.
• The moment expansion of the radial distribution confirms consistency between the full $ R_\Delta $ and the moment-based $ R_4 $, validating the extraction method.
• The results provide essential inputs for chiral extrapolations in lattice $ B $-physics, particularly for form factors and decay amplitudes involving $ D $ and $ B $ mesons.